A quantitative theory for the continuity equation

  • Christian Seis

    Institut für Angewandte Mathematik, Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany


In this work, we provide stability estimates for the continuity equation with Sobolev vector fields. The results are inferred from contraction estimates for certain logarithmic Kantorovich–Rubinstein distances. As a by-product, we obtain a new proof of uniqueness in the DiPerna–Lions setting. The novelty in the proof lies in the fact that it is not based on the theory of renormalized solutions.

Cite this article

Christian Seis, A quantitative theory for the continuity equation. Ann. Inst. H. Poincaré Anal. Non Linéaire 34 (2017), no. 7, pp. 1837–1850

DOI 10.1016/J.ANIHPC.2017.01.001